Abstract-In this work, a design method of an Ultra-Wideband (UWB), low-noise amplifier (LNA) is proposed exerting the performance limitations of a single high-quality discrete transistor. For this purpose, the compatible (Noise F , Input VSWR V i , Gain G T ) triplets and their (Z S , Z L ) terminations of a microwave transistor are exploited for the feasible design target space with the minimum noise F min (f ), maximum gain G T max (f ) and a low input VSWR V i over the available bandwidth B. This multi-objective design procedure is reduced into syntheses of the Darlington equivalences of the Z Sopt (f ), Z L max (f ) terminations with the Unit-elements and short-circuited stubs in the T -, L-, Π-configurations and Particle Swarm Intelligence is successfully implemented as a comparatively simple and efficient optimization tool into both verification of the design target space and the design process of the input and output matching circuits. A typical design example is given with its challenging performance in the simple Π-and Π-configurations realizable by the microstrip line technology. Furthermore the performances of the synthesized amplifiers are compared using an analysis programme in MATLAB code and a microwave system simulator and verified to agree with each other.